Difference between revisions of "Team:INSA-UPS France/Model/Analysis"
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<h1>Model analysis</h1> | <h1>Model analysis</h1> | ||
<p> | <p> | ||
| − | After demonstrating the feasibility of our synthetic consortium, we have characterized some emerging properties that drive its functioning. In particular, we have performed global sensitivity analyses to test the robustness of the system | + | After demonstrating the feasibility of our synthetic consortium, we have characterized some emerging properties that drive its functioning to ultimately improve its efficiency. In particular, we have performed global sensitivity analyses to test the robustness of the system under real life conditions (such as fluctuations of some parameters that can arise from several steps, as detailed below). Then, to optimize its behaviour and guide its design, we carried out more detailed analyses by extending the Metaboloic control analysis framework classically used in the fields of metabolic engeneering and systems biology. |
</p> | </p> | ||
</section> | </section> | ||
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<section> | <section> | ||
<h1>Global sensitivity analysis</h1> | <h1>Global sensitivity analysis</h1> | ||
| − | <p>All parameter values cannot be measured experimentally (1), and our experience in this project, with a model composed by nearly fifty parameters, confirms this fact. As an additional concern, many sources of variability may perturb parameters and ultimately impact the efficiency of the system. Variability could emerge from the system itself (living systems exert some variability by nature) or during each step of the process (manufacturing, transport, storage, etc). Facing this problem, a global sensitivity analysis approach was applied to evaluate the impact of parameters fluctuations on the response time to reach non-pathogenic concentrations.(1) | + | <p>All parameter values cannot be measured experimentally (1), and our experience in this project, with a model composed by nearly fifty parameters, confirms this fact. As an additional concern, many sources of variability may perturb parameters and ultimately impact the efficiency of the system. Variability could emerge from the system itself (living systems exert some variability by nature) or during each step of the process (manufacturing, transport, storage, etc). Facing this problem, a global sensitivity analysis approach was applied to evaluate the impact of random parameters fluctuations on the response time to reach non-pathogenic concentrations.(1) |
</p> | </p> | ||
<p>To perform this analysis, we generated 10,000 sets of parameters randomly sampled within +- 10% of their reference values, using a uniform distribution, and the response time of the system was calculated for each of these sets (Matlab code available below). Simulation results were analyzed with RStudio (R code available below). | <p>To perform this analysis, we generated 10,000 sets of parameters randomly sampled within +- 10% of their reference values, using a uniform distribution, and the response time of the system was calculated for each of these sets (Matlab code available below). Simulation results were analyzed with RStudio (R code available below). | ||
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<img src="https://static.igem.org/mediawiki/2017/b/b5/T--INSA-UPS_France--Global_analysis.png" alt=""> | <img src="https://static.igem.org/mediawiki/2017/b/b5/T--INSA-UPS_France--Global_analysis.png" alt=""> | ||
<figcaption><b>Distribution of the response time for 10,000 sets of random parameters</b></figcaption> | <figcaption><b>Distribution of the response time for 10,000 sets of random parameters</b></figcaption> | ||
| − | <p>Simulation results indicate that the response times varied between 45.46 min (minimum) and 65.05 min (maximum), with a median of 53.70 min and a mean of 53.87 | + | <p>Simulation results indicate that the response times varied between 45.46 min (minimum) and 65.05 min (maximum), with a median of 53.70 min and a mean of 53.87 min close to the response time of the initial set of parameters (53.6 min). The standard deviation of the response time was low (+-3 min).</p> |
<p>These statistical results confirm the global robustness of the system, which will remain efficient even under a reasonable degree of uncertainty. | <p>These statistical results confirm the global robustness of the system, which will remain efficient even under a reasonable degree of uncertainty. | ||
</p> | </p> | ||
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<h1>Metabolic control analysis</h1> | <h1>Metabolic control analysis</h1> | ||
<p> | <p> | ||
| − | <b>Metabolic Control Analysis (MCA)</b> is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them towards each variable of the system.(2)</p><p>Usually applied to investigate the control of concentrations and fluxes under steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on the response time (τ). For each parameter (p), the control coefficient (C) was calculated | + | <b>Metabolic Control Analysis (MCA)</b> is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them towards each variable of the system.(2)</p><p>Usually applied to investigate the control of concentrations and fluxes under steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on the response time (τ). For each parameter (p), the control coefficient (C) was calculated as:</p> |
\begin{equation*} | \begin{equation*} | ||
C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p} | C = \frac{(\tau(p)-\tau(\delta.p))/\tau}{(p - \delta.p)/p} | ||
\end{equation*} | \end{equation*} | ||
| − | <p>This coefficient quantifies the relative change in the response time τ which results from a relative change δ of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time. | + | <p>This coefficient quantifies the relative change in the response time τ which results from a relative change δ of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time. A coefficient of 1 indicate that a change in x% of the parameter results in a change of x% of the response time. |
| − | Control coefficients were calculated by numerical differentiation | + | Control coefficients were calculated by numerical differentiation (δ et at 0.01). This sensitivity analysis was performed for a wide range of initial concentration of <i>Vibrio cholerae</i> to ensure the genericity of its outcome, and results are presented as a heatmap. The Matlab script used to calculated control coefficient and generate the heatmap (SimBiology needed) are available below.</p> |
<p>MCA files: <a href="https://static.igem.org/mediawiki/2017/e/e0/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_MCA.zip" alt="">MCA_ev.m + myEventsFcn.m + System_of_ODEs.m</a></p> | <p>MCA files: <a href="https://static.igem.org/mediawiki/2017/e/e0/T--INSA-UPS_France--iGEM_INSA-UPS_France_2017_MCA.zip" alt="">MCA_ev.m + myEventsFcn.m + System_of_ODEs.m</a></p> | ||
<img src="https://static.igem.org/mediawiki/2017/b/b6/T--INSA-UPS_France--HMnoscale.png" alt=""> | <img src="https://static.igem.org/mediawiki/2017/b/b6/T--INSA-UPS_France--HMnoscale.png" alt=""> | ||
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</li> | </li> | ||
</ul> | </ul> | ||
| − | <p>Important conclusions can be reached from this analysis. First, we notice that the initial concentration in <i>Vibrio harveyi</i> as well as most of its parameters have a weak influence on the response time (coefficients close to 0, | + | <p>Important conclusions can be reached from this analysis. First, we notice that the initial concentration in <i>Vibrio harveyi</i> as well as most of its parameters have a weak influence on the response time (coefficients close to 0, white). <i>V. harveyi</i> works as a simple inducer: a small number of cells is sufficient to sense CAI-1 and produce enough diacetyl to activate <i>Pichia pastoris</i>. On the contrary, <i>Pichia pastoris</i> concentration and other parameters related to the AMP efficiency (MIC50, Vc kill) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill <i>V. cholerae</i>. Efforts to optimize the system by speeding up its response should thus focus in engineering <i>P. pastoris</i> to increase the expression of AMPs, or to improve the efficiency of AMPs, rather than improving the sensor and transmission parts. Interestingly, the device volume also appears to be a key parameters for our system. For further developments, we should consider carefully AMP properties (death rate, IC50 regarding <i>Vibrio cholerae</i>), as well as the AMP expression system <i>Pichia pastoris</i> and its concentration in the device.</p> |
</section> | </section> | ||
<section> | <section> | ||
<h1>Conclusion</h1> | <h1>Conclusion</h1> | ||
| − | <p>Our model analysis gave us promising results about | + | <p>Our model analysis gave us promising results about the efficiency and robustness of the system. |
We demonstrated it shows a robust behaviour under fluctuating conditions, and identified the most controlling parameters that should be tune to improve its response, hence guiding the design of an improved system. | We demonstrated it shows a robust behaviour under fluctuating conditions, and identified the most controlling parameters that should be tune to improve its response, hence guiding the design of an improved system. | ||
| − | <i>Pichia pastoris</i> initial concentration ([<i>Pichia pastoris</i>]<sub>0</sub>) appeared to be the easiest variable to play with, because its value can be directly adapted without any molecular or microbial engineering approach. We thus simulating the response time for a wide range of Pichia pastoris concentrations, and under a wide range of contamination levels (Vibrio cholerae concentration).</p> | + | <i>Pichia pastoris</i> initial concentration ([<i>Pichia pastoris</i>]<sub>0</sub>) appeared to be the easiest variable to play with, because its value can be directly adapted without any molecular or microbial engineering approach. We thus simulating the response time for a wide range of Pichia pastoris concentrations (from XXX to XXX cells), and under a wide range of contamination levels (Vibrio cholerae concentration from 4.10^4 to 10^XXX).</p> |
<img src="https://static.igem.org/mediawiki/2017/a/a8/T--INSA-UPS_France--3Dfig.png" alt=""> | <img src="https://static.igem.org/mediawiki/2017/a/a8/T--INSA-UPS_France--3Dfig.png" alt=""> | ||
<figcaption><b>Response time depending on two major parameters: <i>Vibrio cholerae</i> and <i>Pichia pastoris</i> concentrations</b></figcaption> | <figcaption><b>Response time depending on two major parameters: <i>Vibrio cholerae</i> and <i>Pichia pastoris</i> concentrations</b></figcaption> | ||
| − | <p>Under all the situations tested here, the response time remains below 120 minutes, even at low <i>Pichia pastoris</i> initial concentrations.</p> | + | <p>Under all the situations tested here, the response time remains below 120 minutes, even at low <i>Pichia pastoris</i> initial concentrations and very high <i> V. cholerae</i> levels.</p> |
| − | <p>This two parameters seemed to be the two more | + | <p>This two parameters seemed to be the two more meaningfull to implement in an user-friendly web interface that can be used by non-mathematicians to play with our system.</p> |
<h2><b>→</b> Our visual interface is available on <a href="https://2017.igem.org/Team:INSA-UPS_France/Model/Interface">our interface page</a> | <h2><b>→</b> Our visual interface is available on <a href="https://2017.igem.org/Team:INSA-UPS_France/Model/Interface">our interface page</a> | ||
</section> | </section> | ||
Revision as of 08:17, 19 October 2017
iGEM UPS-INSA Toulouse 2017
Analysis
After demonstrating the feasibility of our synthetic consortium, we have characterized some emerging properties that drive its functioning to ultimately improve its efficiency. In particular, we have performed global sensitivity analyses to test the robustness of the system under real life conditions (such as fluctuations of some parameters that can arise from several steps, as detailed below). Then, to optimize its behaviour and guide its design, we carried out more detailed analyses by extending the Metaboloic control analysis framework classically used in the fields of metabolic engeneering and systems biology.
All parameter values cannot be measured experimentally (1), and our experience in this project, with a model composed by nearly fifty parameters, confirms this fact. As an additional concern, many sources of variability may perturb parameters and ultimately impact the efficiency of the system. Variability could emerge from the system itself (living systems exert some variability by nature) or during each step of the process (manufacturing, transport, storage, etc). Facing this problem, a global sensitivity analysis approach was applied to evaluate the impact of random parameters fluctuations on the response time to reach non-pathogenic concentrations.(1)
To perform this analysis, we generated 10,000 sets of parameters randomly sampled within +- 10% of their reference values, using a uniform distribution, and the response time of the system was calculated for each of these sets (Matlab code available below). Simulation results were analyzed with RStudio (R code available below).
Global analysis files: Global_Analysis.m + System_of_ODEs.m + Resolution_Function.m + myEventsFcn.m + Global_analysis.R Simulation results indicate that the response times varied between 45.46 min (minimum) and 65.05 min (maximum), with a median of 53.70 min and a mean of 53.87 min close to the response time of the initial set of parameters (53.6 min). The standard deviation of the response time was low (+-3 min). These statistical results confirm the global robustness of the system, which will remain efficient even under a reasonable degree of uncertainty.
Metabolic Control Analysis (MCA) is a mathematical tool widely used in biotechnology to quantify the influence of a specific parameter on the functioning of the system, in terms of fluxes and concentrations. Working with a system governed by a large number of parameters, MCA allows to determine the influence of each of them towards each variable of the system.(2) Usually applied to investigate the control of concentrations and fluxes under steady state conditions, we have extended the concepts of MCA to quantify the control exerted by each parameter on the response time (τ). For each parameter (p), the control coefficient (C) was calculated as: This coefficient quantifies the relative change in the response time τ which results from a relative change δ of the parameter p. If the response time is not impacted by a variation of the parameter p, the coefficient will be equal to zero. A positive (negative) value indicates that an increase in p increases (reduces) the response time. A coefficient of 1 indicate that a change in x% of the parameter results in a change of x% of the response time.
Control coefficients were calculated by numerical differentiation (δ et at 0.01). This sensitivity analysis was performed for a wide range of initial concentration of Vibrio cholerae to ensure the genericity of its outcome, and results are presented as a heatmap. The Matlab script used to calculated control coefficient and generate the heatmap (SimBiology needed) are available below. MCA files: MCA_ev.m + myEventsFcn.m + System_of_ODEs.m Important conclusions can be reached from this analysis. First, we notice that the initial concentration in Vibrio harveyi as well as most of its parameters have a weak influence on the response time (coefficients close to 0, white). V. harveyi works as a simple inducer: a small number of cells is sufficient to sense CAI-1 and produce enough diacetyl to activate Pichia pastoris. On the contrary, Pichia pastoris concentration and other parameters related to the AMP efficiency (MIC50, Vc kill) have a significant impact on the response time, because a high antimicrobial peptides (AMP) concentration is required to kill V. cholerae. Efforts to optimize the system by speeding up its response should thus focus in engineering P. pastoris to increase the expression of AMPs, or to improve the efficiency of AMPs, rather than improving the sensor and transmission parts. Interestingly, the device volume also appears to be a key parameters for our system. For further developments, we should consider carefully AMP properties (death rate, IC50 regarding Vibrio cholerae), as well as the AMP expression system Pichia pastoris and its concentration in the device. Our model analysis gave us promising results about the efficiency and robustness of the system.
We demonstrated it shows a robust behaviour under fluctuating conditions, and identified the most controlling parameters that should be tune to improve its response, hence guiding the design of an improved system.
Pichia pastoris initial concentration ([Pichia pastoris]0) appeared to be the easiest variable to play with, because its value can be directly adapted without any molecular or microbial engineering approach. We thus simulating the response time for a wide range of Pichia pastoris concentrations (from XXX to XXX cells), and under a wide range of contamination levels (Vibrio cholerae concentration from 4.10^4 to 10^XXX). Under all the situations tested here, the response time remains below 120 minutes, even at low Pichia pastoris initial concentrations and very high V. cholerae levels. This two parameters seemed to be the two more meaningfull to implement in an user-friendly web interface that can be used by non-mathematicians to play with our system.
Model analysis
Global sensitivity analysis
Metabolic control analysis
Conclusion
→ Our visual interface is available on our interface page
References
